LMFDB - Embedded newform 560.2.ci.c.353.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [560,2,Mod(17,560)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(560, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 0, 3, 2]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("560.17");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 560 = 2^{4} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	560.ci (of order $12$, degree $4$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$4.47162251319$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{12})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 10x^{14} + 61x^{12} + 266x^{10} + 852x^{8} + 1438x^{6} + 1933x^{4} + 3038x^{2} + 2401 $ x^16 + 10x^14 + 61x^12 + 266x^10 + 852x^8 + 1438x^6 + 1933x^4 + 3038*x^2 + 2401
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 70)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			353.2
Root			$1.45333 - 1.51725i$ of defining polynomial
Character	$\chi$	$=$	560.353
Dual form			560.2.ci.c.257.2

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.304013 - 1.13459i) q^{3} +(-1.79038 - 1.33961i) q^{5} +(2.55176 + 0.698943i) q^{7} +(1.40320 - 0.810140i) q^{9} +O(q^{10})$	\(q+(-0.304013 - 1.13459i) q^{3} +(-1.79038 - 1.33961i) q^{5} +(2.55176 + 0.698943i) q^{7} +(1.40320 - 0.810140i) q^{9} +(0.371536 - 0.643519i) q^{11} +(2.05532 - 2.05532i) q^{13} +(-0.975610 + 2.43860i) q^{15} +(-6.33660 + 1.69789i) q^{17} +(-0.946027 - 1.63857i) q^{19} +(0.0172465 - 3.10769i) q^{21} +(1.36952 - 5.11112i) q^{23} +(1.41090 + 4.79681i) q^{25} +(-3.83750 - 3.83750i) q^{27} -9.69135i q^{29} +(-2.96403 - 1.71129i) q^{31} +(-0.843083 - 0.225903i) q^{33} +(-3.63230 - 4.66973i) q^{35} +(2.58012 + 0.691342i) q^{37} +(-2.95680 - 1.70711i) q^{39} +0.817699i q^{41} +(-1.59589 - 1.59589i) q^{43} +(-3.59753 - 0.429287i) q^{45} +(-1.21894 + 4.54913i) q^{47} +(6.02296 + 3.56707i) q^{49} +(3.85282 + 6.67328i) q^{51} +(-4.81583 + 1.29040i) q^{53} +(-1.52725 + 0.654429i) q^{55} +(-1.57150 + 1.57150i) q^{57} +(1.27487 - 2.20815i) q^{59} +(5.25989 - 3.03680i) q^{61} +(4.14688 - 1.08652i) q^{63} +(-6.43313 + 0.926476i) q^{65} +(3.54358 + 13.2248i) q^{67} -6.21538 q^{69} +16.0173 q^{71} +(-2.29071 - 8.54906i) q^{73} +(5.01348 - 3.05909i) q^{75} +(1.39785 - 1.38242i) q^{77} +(5.70091 - 3.29142i) q^{79} +(-0.756928 + 1.31104i) q^{81} +(-9.23519 + 9.23519i) q^{83} +(13.6194 + 5.44871i) q^{85} +(-10.9957 + 2.94629i) q^{87} +(3.01603 + 5.22392i) q^{89} +(6.68124 - 3.80814i) q^{91} +(-1.04051 + 3.88322i) q^{93} +(-0.501292 + 4.20096i) q^{95} +(3.16693 + 3.16693i) q^{97} -1.20398i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 12 q^{5} - 8 q^{7}+O(q^{10}) $ 16 * q - 12 * q^5 - 8 * q^7	$ 16 q - 12 q^{5} - 8 q^{7} + 12 q^{11} - 16 q^{15} - 36 q^{17} - 28 q^{21} + 4 q^{23} + 12 q^{25} - 24 q^{31} + 48 q^{33} - 8 q^{35} + 4 q^{37} + 8 q^{43} - 12 q^{45} - 12 q^{47} + 16 q^{51} - 28 q^{53} + 8 q^{57} - 12 q^{61} + 36 q^{63} - 8 q^{65} - 32 q^{67} - 16 q^{71} - 12 q^{73} + 48 q^{75} + 16 q^{77} + 24 q^{85} + 24 q^{87} + 16 q^{91} + 28 q^{93} - 20 q^{95}+O(q^{100}) $ 16 * q - 12 * q^5 - 8 * q^7 + 12 * q^11 - 16 * q^15 - 36 * q^17 - 28 * q^21 + 4 * q^23 + 12 * q^25 - 24 * q^31 + 48 * q^33 - 8 * q^35 + 4 * q^37 + 8 * q^43 - 12 * q^45 - 12 * q^47 + 16 * q^51 - 28 * q^53 + 8 * q^57 - 12 * q^61 + 36 * q^63 - 8 * q^65 - 32 * q^67 - 16 * q^71 - 12 * q^73 + 48 * q^75 + 16 * q^77 + 24 * q^85 + 24 * q^87 + 16 * q^91 + 28 * q^93 - 20 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/560\mathbb{Z}\right)^\times$.

$n$	$241$	$337$	$351$	$421$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{3}{4}\right)$	$1$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		0			0
$2$		0			0
$3$	−0.304013	−	1.13459i	−0.175522	−	0.655056i	−0.996462	−	0.0840425i	$-0.973217\pi$
$3$	−0.304013	−	1.13459i	−0.175522	−	0.655056i	0.820940	−	0.571014i	$-0.193450\pi$
$4$		0			0
$5$	−1.79038	−	1.33961i	−0.800681	−	0.599091i
$5$	−1.79038	−	1.33961i	−0.800681	−	0.599091i
$6$		0			0
$7$	2.55176	+	0.698943i	0.964475	+	0.264175i
$7$	2.55176	+	0.698943i	0.964475	+	0.264175i
$8$		0			0
$9$	1.40320	−	0.810140i	0.467734	−	0.270047i
$10$		0			0
$11$	0.371536	−	0.643519i	0.112022	−	0.194028i	−0.804563	−	0.593867i	$-0.797601\pi$
$11$	0.371536	−	0.643519i	0.112022	−	0.194028i	0.916586	+	0.399839i	$0.130934\pi$
$12$		0			0
$13$	2.05532	−	2.05532i	0.570044	−	0.570044i	−0.362097	−	0.932141i	$-0.617939\pi$
$13$	2.05532	−	2.05532i	0.570044	−	0.570044i	0.932141	+	0.362097i	$0.117939\pi$
$14$		0			0
$15$	−0.975610	+	2.43860i	−0.251901	+	0.629645i
$16$		0			0
$17$	−6.33660	+	1.69789i	−1.53685	+	0.411798i	−0.925247	−	0.379365i	$-0.876143\pi$
$17$	−6.33660	+	1.69789i	−1.53685	+	0.411798i	−0.611605	+	0.791163i	$0.709476\pi$
$18$		0			0
$19$	−0.946027	−	1.63857i	−0.217033	−	0.375913i	0.736866	−	0.676039i	$-0.236305\pi$
$19$	−0.946027	−	1.63857i	−0.217033	−	0.375913i	−0.953900	+	0.300126i	$0.902971\pi$
$20$		0			0
$21$	0.0172465	−	3.10769i	0.00376349	−	0.678154i
$22$		0			0
$23$	1.36952	−	5.11112i	0.285565	−	1.06574i	−0.662861	−	0.748743i	$-0.730658\pi$
$23$	1.36952	−	5.11112i	0.285565	−	1.06574i	0.948426	−	0.317000i	$-0.102675\pi$
$24$		0			0
$25$	1.41090	+	4.79681i	0.282180	+	0.959361i
$26$		0			0
$27$	−3.83750	−	3.83750i	−0.738528	−	0.738528i
$28$		0			0
$29$		−	9.69135i		−	1.79964i	−0.436263	−	0.899819i	$-0.643698\pi$
$29$		−	9.69135i		−	1.79964i	0.436263	−	0.899819i	$-0.356302\pi$
$30$		0			0
$31$	−2.96403	−	1.71129i	−0.532356	−	0.307356i	0.209619	−	0.977783i	$-0.432778\pi$
$31$	−2.96403	−	1.71129i	−0.532356	−	0.307356i	−0.741975	+	0.670427i	$0.766111\pi$
$32$		0			0
$33$	−0.843083	−	0.225903i	−0.146762	−	0.0393247i
$34$		0			0
$35$	−3.63230	−	4.66973i	−0.613971	−	0.789328i
$36$		0			0
$37$	2.58012	+	0.691342i	0.424170	+	0.113656i	0.464588	−	0.885527i	$-0.346202\pi$
$37$	2.58012	+	0.691342i	0.424170	+	0.113656i	−0.0404183	+	0.999183i	$0.512869\pi$
$38$		0			0
$39$	−2.95680	−	1.70711i	−0.473466	−	0.273356i
$40$		0			0
$41$			0.817699i			0.127703i	0.997959	+	0.0638515i	$0.0203384\pi$
$41$			0.817699i			0.127703i	−0.997959	+	0.0638515i	$0.979662\pi$
$42$		0			0
$43$	−1.59589	−	1.59589i	−0.243371	−	0.243371i	0.574872	−	0.818243i	$-0.305052\pi$
$43$	−1.59589	−	1.59589i	−0.243371	−	0.243371i	−0.818243	+	0.574872i	$0.805052\pi$
$44$		0			0
$45$	−3.59753	−	0.429287i	−0.536288	−	0.0639943i
$46$		0			0
$47$	−1.21894	+	4.54913i	−0.177800	+	0.663560i	0.818257	+	0.574852i	$0.194940\pi$
$47$	−1.21894	+	4.54913i	−0.177800	+	0.663560i	−0.996058	+	0.0887076i	$0.971726\pi$
$48$		0			0
$49$	6.02296	+	3.56707i	0.860423	+	0.509581i
$50$		0			0
$51$	3.85282	+	6.67328i	0.539502	+	0.934445i
$52$		0			0
$53$	−4.81583	+	1.29040i	−0.661505	+	0.177250i	−0.573925	−	0.818908i	$-0.694580\pi$
$53$	−4.81583	+	1.29040i	−0.661505	+	0.177250i	−0.0875798	+	0.996158i	$0.527913\pi$
$54$		0			0
$55$	−1.52725	+	0.654429i	−0.205935	+	0.0882432i
$56$		0			0
$57$	−1.57150	+	1.57150i	−0.208150	+	0.208150i
$58$		0			0
$59$	1.27487	−	2.20815i	0.165975	−	0.287476i	−0.771026	−	0.636803i	$-0.780256\pi$
$59$	1.27487	−	2.20815i	0.165975	−	0.287476i	0.937001	+	0.349327i	$0.113590\pi$
$60$		0			0
$61$	5.25989	−	3.03680i	0.673460	−	0.388822i	−0.123927	−	0.992291i	$-0.539549\pi$
$61$	5.25989	−	3.03680i	0.673460	−	0.388822i	0.797386	+	0.603469i	$0.206215\pi$
$62$		0			0
$63$	4.14688	−	1.08652i	0.522458	−	0.136889i
$64$		0			0
$65$	−6.43313	+	0.926476i	−0.797932	+	0.114915i
$66$		0			0
$67$	3.54358	+	13.2248i	0.432917	+	1.61567i	0.746002	+	0.665944i	$0.231971\pi$
$67$	3.54358	+	13.2248i	0.432917	+	1.61567i	−0.313084	+	0.949725i	$0.601362\pi$
$68$		0			0
$69$	−6.21538			−0.748244
$70$		0			0
$71$	16.0173			1.90090			0.950450	−	0.310879i	$-0.100623\pi$
$71$	16.0173			1.90090			0.950450	+	0.310879i	$0.100623\pi$
$72$		0			0
$73$	−2.29071	−	8.54906i	−0.268108	−	1.00059i	−0.960321	−	0.278898i	$-0.910031\pi$
$73$	−2.29071	−	8.54906i	−0.268108	−	1.00059i	0.692213	−	0.721693i	$-0.256636\pi$
$74$		0			0
$75$	5.01348	−	3.05909i	0.578907	−	0.353233i
$76$		0			0
$77$	1.39785	−	1.38242i	0.159300	−	0.157542i
$78$		0			0
$79$	5.70091	−	3.29142i	0.641402	−	0.370314i	−0.143752	−	0.989614i	$-0.545917\pi$
$79$	5.70091	−	3.29142i	0.641402	−	0.370314i	0.785155	+	0.619300i	$0.212583\pi$
$80$		0			0
$81$	−0.756928	+	1.31104i	−0.0841031	+	0.145671i
$82$		0			0
$83$	−9.23519	+	9.23519i	−1.01369	+	1.01369i	−0.0137887	+	0.999905i	$0.504389\pi$
$83$	−9.23519	+	9.23519i	−1.01369	+	1.01369i	−0.999905	+	0.0137887i	$0.995611\pi$
$84$		0			0
$85$	13.6194	+	5.44871i	1.47723	+	0.590995i
$86$		0			0
$87$	−10.9957	+	2.94629i	−1.17886	+	0.315876i
$88$		0			0
$89$	3.01603	+	5.22392i	0.319699	+	0.553735i	0.980425	−	0.196892i	$-0.0630849\pi$
$89$	3.01603	+	5.22392i	0.319699	+	0.553735i	−0.660726	+	0.750627i	$0.729752\pi$
$90$		0			0
$91$	6.68124	−	3.80814i	0.700385	−	0.399201i
$92$		0			0
$93$	−1.04051	+	3.88322i	−0.107895	+	0.402671i
$94$		0			0
$95$	−0.501292	+	4.20096i	−0.0514315	+	0.431009i
$96$		0			0
$97$	3.16693	+	3.16693i	0.321553	+	0.321553i	0.849363	−	0.527810i	$-0.176987\pi$
$97$	3.16693	+	3.16693i	0.321553	+	0.321553i	−0.527810	+	0.849363i	$0.676987\pi$
$98$		0			0
$99$		−	1.20398i		−	0.121005i
$100$		0			0
$101$	9.68359	+	5.59083i	0.963554	+	0.556308i	0.897265	−	0.441493i	$-0.145551\pi$
$101$	9.68359	+	5.59083i	0.963554	+	0.556308i	0.0662887	+	0.997800i	$0.478884\pi$
$102$		0			0
$103$	−2.34351	−	0.627940i	−0.230912	−	0.0618728i	0.141507	−	0.989937i	$-0.454805\pi$
$103$	−2.34351	−	0.627940i	−0.230912	−	0.0618728i	−0.372420	+	0.928064i	$0.621472\pi$
$104$		0			0
$105$	−4.19397	+	5.54084i	−0.409289	+	0.540730i
$106$		0			0
$107$	−6.41422	−	1.71868i	−0.620086	−	0.166151i	−0.0649189	−	0.997891i	$-0.520679\pi$
$107$	−6.41422	−	1.71868i	−0.620086	−	0.166151i	−0.555167	+	0.831739i	$0.687346\pi$
$108$		0			0
$109$	−7.76000	−	4.48024i	−0.743274	−	0.429129i	0.0799848	−	0.996796i	$-0.474513\pi$
$109$	−7.76000	−	4.48024i	−0.743274	−	0.429129i	−0.823258	+	0.567667i	$0.807846\pi$
$110$		0			0
$111$		−	3.13756i		−	0.297804i
$112$		0			0
$113$	0.307790	+	0.307790i	0.0289545	+	0.0289545i	0.721436	−	0.692481i	$-0.243482\pi$
$113$	0.307790	+	0.307790i	0.0289545	+	0.0289545i	−0.692481	+	0.721436i	$0.743482\pi$
$114$		0			0
$115$	−9.29886	+	7.31621i	−0.867123	+	0.682240i
$116$		0			0
$117$	1.21894	−	4.54913i	0.112691	−	0.420568i
$118$		0			0
$119$	−17.3562	−	0.0963204i	−1.59104	−	0.00882967i
$120$		0			0
$121$	5.22392	+	9.04810i	0.474902	+	0.822554i
$122$		0			0
$123$	0.927753	−	0.248591i	0.0836527	−	0.0224147i
$124$		0			0
$125$	3.89980	−	10.4781i	0.348808	−	0.937194i
$126$		0			0
$127$	11.1823	−	11.1823i	0.992267	−	0.992267i	−0.00770296	−	0.999970i	$-0.502452\pi$
$127$	11.1823	−	11.1823i	0.992267	−	0.992267i	0.999970	+	0.00770296i	$0.00245195\pi$
$128$		0			0
$129$	−1.32551	+	2.29585i	−0.116705	+	0.202139i
$130$		0			0
$131$	8.30763	−	4.79641i	0.725841	−	0.419064i	−0.0910579	−	0.995846i	$-0.529025\pi$
$131$	8.30763	−	4.79641i	0.725841	−	0.419064i	0.816899	+	0.576781i	$0.195692\pi$
$132$		0			0
$133$	−1.26877	−	4.84245i	−0.110016	−	0.419893i
$134$		0			0
$135$	1.72983	+	12.0113i	0.148880	+	1.03377i
$136$		0			0
$137$	2.40949	+	8.99233i	0.205856	+	0.768267i	0.989187	+	0.146661i	$0.0468526\pi$
$137$	2.40949	+	8.99233i	0.205856	+	0.768267i	−0.783330	+	0.621606i	$0.786481\pi$
$138$		0			0
$139$	22.1714			1.88056			0.940278	−	0.340408i	$-0.110565\pi$
$139$	22.1714			1.88056			0.940278	+	0.340408i	$0.110565\pi$
$140$		0			0
$141$	5.53198			0.465877
$142$		0			0
$143$	−0.559013	−	2.08627i	−0.0467470	−	0.174462i
$144$		0			0
$145$	−12.9826	+	17.3512i	−1.07815	+	1.44094i
$146$		0			0
$147$	2.21611	−	7.91803i	0.182781	−	0.653068i
$148$		0			0
$149$	3.41418	−	1.97118i	0.279701	−	0.161485i	−0.353587	−	0.935402i	$-0.615038\pi$
$149$	3.41418	−	1.97118i	0.279701	−	0.161485i	0.633288	+	0.773916i	$0.281705\pi$
$150$		0			0
$151$	−9.97267	+	17.2732i	−0.811564	+	1.40567i	0.100205	+	0.994967i	$0.468050\pi$
$151$	−9.97267	+	17.2732i	−0.811564	+	1.40567i	−0.911769	+	0.410703i	$0.865283\pi$
$152$		0			0
$153$	−7.51602	+	7.51602i	−0.607634	+	0.607634i
$154$		0			0
$155$	3.01429	+	7.03449i	0.242113	+	0.565024i
$156$		0			0
$157$	−7.20903	+	1.93165i	−0.575343	+	0.154163i	−0.534746	−	0.845013i	$-0.679593\pi$
$157$	−7.20903	+	1.93165i	−0.575343	+	0.154163i	−0.0405972	+	0.999176i	$0.512926\pi$
$158$		0			0
$159$	2.92815	+	5.07170i	0.232217	+	0.402212i
$160$		0			0
$161$	7.06707	−	12.0851i	0.556963	−	0.952442i
$162$		0			0
$163$	−3.14893	+	11.7520i	−0.246644	+	0.920486i	0.725907	+	0.687793i	$0.241420\pi$
$163$	−3.14893	+	11.7520i	−0.246644	+	0.920486i	−0.972550	+	0.232693i	$0.925246\pi$
$164$		0			0
$165$	1.20681	+	1.53385i	0.0939503	+	0.119410i
$166$		0			0
$167$	−1.45564	−	1.45564i	−0.112641	−	0.112641i	0.648540	−	0.761181i	$-0.275380\pi$
$167$	−1.45564	−	1.45564i	−0.112641	−	0.112641i	−0.761181	+	0.648540i	$0.775380\pi$
$168$		0			0
$169$			4.55129i			0.350099i
$170$		0			0
$171$	−2.65494	−	1.53283i	−0.203028	−	0.117218i
$172$		0			0
$173$	9.08750	+	2.43499i	0.690910	+	0.185129i	0.587155	−	0.809474i	$-0.300248\pi$
$173$	9.08750	+	2.43499i	0.690910	+	0.185129i	0.103754	+	0.994603i	$0.466914\pi$
$174$		0			0
$175$	0.247587	+	13.2264i	0.0187158	+	0.999825i
$176$		0			0
$177$	−2.89292	−	0.775156i	−0.217445	−	0.0582643i
$178$		0			0
$179$	−3.89494	−	2.24874i	−0.291121	−	0.168079i	0.347326	−	0.937744i	$-0.387090\pi$
$179$	−3.89494	−	2.24874i	−0.291121	−	0.168079i	−0.638447	+	0.769665i	$0.720423\pi$
$180$		0			0
$181$			17.8850i			1.32938i	0.747118	+	0.664691i	$0.231437\pi$
$181$			17.8850i			1.32938i	−0.747118	+	0.664691i	$0.768563\pi$
$182$		0			0
$183$	−5.04460	−	5.04460i	−0.372907	−	0.372907i
$184$		0			0
$185$	−3.69327	−	4.69412i	−0.271535	−	0.345119i
$186$		0			0
$187$	−1.26165	+	4.70855i	−0.0922612	+	0.344323i
$188$		0			0
$189$	−7.11019	−	12.4746i	−0.517190	−	0.907392i
$190$		0			0
$191$	−1.38774	−	2.40364i	−0.100413	−	0.173921i	0.811442	−	0.584433i	$-0.198683\pi$
$191$	−1.38774	−	2.40364i	−0.100413	−	0.173921i	−0.911855	+	0.410512i	$0.865350\pi$
$192$		0			0
$193$	4.96491	−	1.33034i	0.357382	−	0.0957602i	−0.0756607	−	0.997134i	$-0.524107\pi$
$193$	4.96491	−	1.33034i	0.357382	−	0.0957602i	0.433043	+	0.901373i	$0.357440\pi$
$194$		0			0
$195$	3.00693	+	7.01731i	0.215330	+	0.502520i
$196$		0			0
$197$	1.34043	−	1.34043i	0.0955019	−	0.0955019i	−0.657742	−	0.753244i	$-0.728488\pi$
$197$	1.34043	−	1.34043i	0.0955019	−	0.0955019i	0.753244	+	0.657742i	$0.228488\pi$
$198$		0			0
$199$	7.25148	−	12.5599i	0.514043	−	0.890349i	−0.485824	−	0.874057i	$-0.661480\pi$
$199$	7.25148	−	12.5599i	0.514043	−	0.890349i	0.999867	−	0.0162926i	$-0.00518634\pi$
$200$		0			0
$201$	13.9275	−	8.04103i	0.982368	−	0.567171i
$202$		0			0
$203$	6.77370	−	24.7300i	0.475420	−	1.73571i
$204$		0			0
$205$	1.09540	−	1.46399i	0.0765057	−	0.102249i
$206$		0			0
$207$	−2.21901	−	8.28144i	−0.154232	−	0.575600i
$208$		0			0
$209$	−1.40593			−0.0972504
$210$		0			0
$211$	−10.0324			−0.690660			−0.345330	−	0.938481i	$-0.612233\pi$
$211$	−10.0324			−0.690660			−0.345330	+	0.938481i	$0.612233\pi$
$212$		0			0
$213$	−4.86945	−	18.1730i	−0.333649	−	1.24520i
$214$		0			0
$215$	0.719378	+	4.99511i	0.0490611	+	0.340664i
$216$		0			0
$217$	−6.36741	−	6.43848i	−0.432248	−	0.437073i
$218$		0			0
$219$	−9.00328	+	5.19804i	−0.608385	+	0.351251i
$220$		0			0
$221$	−9.53406	+	16.5135i	−0.641330	+	1.11082i
$222$		0			0
$223$	3.13756	−	3.13756i	0.210107	−	0.210107i	−0.594206	−	0.804313i	$-0.702534\pi$
$223$	3.13756	−	3.13756i	0.210107	−	0.210107i	0.804313	+	0.594206i	$0.202534\pi$
$224$		0			0
$225$	5.86586	+	5.58787i	0.391058	+	0.372525i
$226$		0			0
$227$	−0.648012	+	0.173634i	−0.0430101	+	0.0115245i	−0.280260	−	0.959924i	$-0.590421\pi$
$227$	−0.648012	+	0.173634i	−0.0430101	+	0.0115245i	0.237250	+	0.971449i	$0.423754\pi$
$228$		0			0
$229$	−6.60166	−	11.4344i	−0.436250	−	0.755608i	0.561146	−	0.827717i	$-0.310360\pi$
$229$	−6.60166	−	11.4344i	−0.436250	−	0.755608i	−0.997397	+	0.0721088i	$0.977027\pi$
$230$		0			0
$231$	−1.99345	−	1.16572i	−0.131159	−	0.0766986i
$232$		0			0
$233$	−2.24110	+	8.36389i	−0.146819	+	0.547937i	0.852849	+	0.522158i	$0.174873\pi$
$233$	−2.24110	+	8.36389i	−0.146819	+	0.547937i	−0.999668	+	0.0257782i	$0.991794\pi$
$234$		0			0
$235$	8.27641	−	6.51177i	0.539894	−	0.424781i
$236$		0			0
$237$	−5.46757	−	5.46757i	−0.355157	−	0.355157i
$238$		0			0
$239$			4.00294i			0.258929i	0.991584	+	0.129464i	$0.0413258\pi$
$239$			4.00294i			0.258929i	−0.991584	+	0.129464i	$0.958674\pi$
$240$		0			0
$241$	−15.0040	−	8.66256i	−0.966493	−	0.558005i	−0.0683274	−	0.997663i	$-0.521766\pi$
$241$	−15.0040	−	8.66256i	−0.966493	−	0.558005i	−0.898165	+	0.439658i	$0.855100\pi$
$242$		0			0
$243$	−14.0088	−	3.75364i	−0.898663	−	0.240796i
$244$		0			0
$245$	−6.00489	−	14.4548i	−0.383639	−	0.923483i
$246$		0			0
$247$	−5.31218	−	1.42339i	−0.338006	−	0.0905683i
$248$		0			0
$249$	13.2858	+	7.67055i	0.841952	+	0.486101i
$250$		0			0
$251$			5.49938i			0.347118i	0.984824	+	0.173559i	$0.0555267\pi$
$251$			5.49938i			0.347118i	−0.984824	+	0.173559i	$0.944473\pi$
$252$		0			0
$253$	−2.78028	−	2.78028i	−0.174795	−	0.174795i
$254$		0			0
$255$	2.04158	−	17.1089i	0.127849	−	1.07140i
$256$		0			0
$257$	4.27307	−	15.9473i	0.266547	−	0.994766i	−0.694750	−	0.719251i	$-0.744485\pi$
$257$	4.27307	−	15.9473i	0.266547	−	0.994766i	0.961297	−	0.275515i	$-0.0888483\pi$
$258$		0			0
$259$	6.10065	+	3.56750i	0.379076	+	0.221674i
$260$		0			0
$261$	−7.85135	−	13.5989i	−0.485986	−	0.841753i
$262$		0			0
$263$	−9.52484	+	2.55217i	−0.587327	+	0.157374i	−0.540231	−	0.841517i	$-0.681663\pi$
$263$	−9.52484	+	2.55217i	−0.587327	+	0.157374i	−0.0470956	+	0.998890i	$0.514997\pi$
$264$		0			0
$265$	10.3508	+	4.14102i	0.635843	+	0.254381i
$266$		0			0
$267$	5.01010	−	5.01010i	0.306613	−	0.306613i
$268$		0			0
$269$	−4.47922	+	7.75824i	−0.273103	+	0.473028i	−0.969655	−	0.244478i	$-0.921383\pi$
$269$	−4.47922	+	7.75824i	−0.273103	+	0.473028i	0.696552	+	0.717506i	$0.254717\pi$
$270$		0			0
$271$	19.7889	−	11.4251i	1.20209	−	0.694027i	0.241071	−	0.970507i	$-0.422501\pi$
$271$	19.7889	−	11.4251i	1.20209	−	0.694027i	0.961020	+	0.276480i	$0.0891680\pi$
$272$		0			0
$273$	−6.35186	−	6.42276i	−0.384432	−	0.388723i
$274$		0			0
$275$	3.61104	+	0.874245i	0.217754	+	0.0527189i
$276$		0			0
$277$	5.57320	+	20.7995i	0.334861	+	1.24972i	0.904019	+	0.427491i	$0.140603\pi$
$277$	5.57320	+	20.7995i	0.334861	+	1.24972i	−0.569158	+	0.822228i	$0.692731\pi$
$278$		0			0
$279$	−5.54552			−0.332002
$280$		0			0
$281$	−5.64885			−0.336982			−0.168491	−	0.985703i	$-0.553889\pi$
$281$	−5.64885			−0.336982			−0.168491	+	0.985703i	$0.553889\pi$
$282$		0			0
$283$	0.757948	+	2.82870i	0.0450553	+	0.168149i	0.984788	−	0.173762i	$-0.0555925\pi$
$283$	0.757948	+	2.82870i	0.0450553	+	0.168149i	−0.939732	+	0.341911i	$0.888926\pi$
$284$		0			0
$285$	4.91877	−	0.708383i	0.291363	−	0.0419610i
$286$		0			0
$287$	−0.571524	+	2.08657i	−0.0337360	+	0.123166i
$288$		0			0
$289$	22.5473	−	13.0177i	1.32631	−	0.765747i
$290$		0			0
$291$	2.63038	−	4.55596i	0.154196	−	0.267075i
$292$		0			0
$293$	10.7875	−	10.7875i	0.630212	−	0.630212i	−0.317909	−	0.948121i	$-0.602981\pi$
$293$	10.7875	−	10.7875i	0.630212	−	0.630212i	0.948121	+	0.317909i	$0.102981\pi$
$294$		0			0
$295$	−5.24056	+	2.24558i	−0.305117	+	0.130743i
$296$		0			0
$297$	−3.89528	+	1.04374i	−0.226027	+	0.0605637i
$298$		0			0
$299$	−7.69020	−	13.3198i	−0.444736	−	0.770305i
$300$		0			0
$301$	−2.95689	−	5.18776i	−0.170432	−	0.299018i
$302$		0			0
$303$	3.39936	−	12.6866i	0.195288	−	0.728826i
$304$		0			0
$305$	−13.4853	−	1.60917i	−0.772166	−	0.0921411i
$306$		0			0
$307$	6.89201	+	6.89201i	0.393348	+	0.393348i	0.875879	−	0.482531i	$-0.160282\pi$
$307$	6.89201	+	6.89201i	0.393348	+	0.393348i	−0.482531	+	0.875879i	$0.660282\pi$
$308$		0			0
$309$			2.84982i			0.162121i
$310$		0			0
$311$	0.109136	+	0.0630096i	0.00618852	+	0.00357294i	0.503091	−	0.864233i	$-0.332196\pi$
$311$	0.109136	+	0.0630096i	0.00618852	+	0.00357294i	−0.496903	+	0.867806i	$0.665529\pi$
$312$		0			0
$313$	−11.2955	−	3.02662i	−0.638459	−	0.171075i	−0.0749536	−	0.997187i	$-0.523881\pi$
$313$	−11.2955	−	3.02662i	−0.638459	−	0.171075i	−0.563505	+	0.826112i	$0.690548\pi$
$314$		0			0
$315$	−8.87999	−	3.60991i	−0.500331	−	0.203395i
$316$		0			0
$317$	10.5732	+	2.83308i	0.593851	+	0.159122i	0.543212	−	0.839595i	$-0.317208\pi$
$317$	10.5732	+	2.83308i	0.593851	+	0.159122i	0.0506382	+	0.998717i	$0.483874\pi$
$318$		0			0
$319$	−6.23657	−	3.60068i	−0.349181	−	0.201600i
$320$		0			0
$321$			7.80001i			0.435354i
$322$		0			0
$323$	8.77670	+	8.77670i	0.488349	+	0.488349i
$324$		0			0
$325$	12.7588	+	6.95913i	0.707733	+	0.386023i
$326$		0			0
$327$	−2.72410	+	10.1665i	−0.150643	+	0.562208i
$328$		0			0
$329$	−6.29002	+	10.7563i	−0.346780	+	0.593016i
$330$		0			0
$331$	−2.73019	−	4.72883i	−0.150065	−	0.259920i	0.781186	−	0.624298i	$-0.214615\pi$
$331$	−2.73019	−	4.72883i	−0.150065	−	0.259920i	−0.931251	+	0.364378i	$0.881282\pi$
$332$		0			0
$333$	4.18052	−	1.12017i	0.229091	−	0.0613848i
$334$		0			0
$335$	11.3717	−	28.4244i	0.621304	−	1.55299i
$336$		0			0
$337$	20.4823	−	20.4823i	1.11574	−	1.11574i	0.123385	−	0.992359i	$-0.460625\pi$
$337$	20.4823	−	20.4823i	1.11574	−	1.11574i	0.992359	−	0.123385i	$-0.0393751\pi$
$338$		0			0
$339$	0.255644	−	0.442788i	0.0138847	−	0.0240490i
$340$		0			0
$341$	−2.20249	+	1.27161i	−0.119272	+	0.0688615i
$342$		0			0
$343$	12.8760	+	13.3120i	0.695237	+	0.718781i
$344$		0			0
$345$	11.1279	+	8.32618i	0.599105	+	0.448266i
$346$		0			0
$347$	5.57442	+	20.8040i	0.299250	+	1.11682i	0.937783	+	0.347223i	$0.112875\pi$
$347$	5.57442	+	20.8040i	0.299250	+	1.11682i	−0.638532	+	0.769595i	$0.720458\pi$
$348$		0			0
$349$	12.5744			0.673093			0.336546	−	0.941667i	$-0.390741\pi$
$349$	12.5744			0.673093			0.336546	+	0.941667i	$0.390741\pi$
$350$		0			0
$351$	−15.7746			−0.841987
$352$		0			0
$353$	0.178457	+	0.666012i	0.00949832	+	0.0354482i	0.970512	−	0.241051i	$-0.0774922\pi$
$353$	0.178457	+	0.666012i	0.00949832	+	0.0354482i	−0.961014	+	0.276500i	$0.910826\pi$
$354$		0			0
$355$	−28.6769	−	21.4569i	−1.52201	−	1.13881i
$356$		0			0
$357$	5.16723	+	19.7215i	0.273479	+	1.04377i
$358$		0			0
$359$	19.1381	−	11.0494i	1.01007	−	0.583165i	0.0988582	−	0.995102i	$-0.468481\pi$
$359$	19.1381	−	11.0494i	1.01007	−	0.583165i	0.911212	+	0.411937i	$0.135148\pi$
$360$		0			0
$361$	7.71007	−	13.3542i	0.405793	−	0.702854i
$362$		0			0
$363$	8.67775	−	8.67775i	0.455464	−	0.455464i
$364$		0			0
$365$	−7.35115	+	18.3747i	−0.384777	+	0.961775i
$366$		0			0
$367$	−12.9539	+	3.47100i	−0.676191	+	0.181185i	−0.580542	−	0.814230i	$-0.697159\pi$
$367$	−12.9539	+	3.47100i	−0.676191	+	0.181185i	−0.0956487	+	0.995415i	$0.530493\pi$
$368$		0			0
$369$	0.662450	+	1.14740i	0.0344858	+	0.0597311i
$370$		0			0
$371$	−13.1908	−	0.0732036i	−0.684830	−	0.00380054i
$372$		0			0
$373$	−3.87359	+	14.4564i	−0.200567	+	0.748526i	0.790188	+	0.612864i	$0.209983\pi$
$373$	−3.87359	+	14.4564i	−0.200567	+	0.748526i	−0.990755	+	0.135662i	$0.956684\pi$
$374$		0			0
$375$	−13.0740	−	1.23918i	−0.675138	−	0.0639912i
$376$		0			0
$377$	−19.9189	−	19.9189i	−1.02587	−	1.02587i
$378$		0			0
$379$			1.71784i			0.0882395i	0.999026	+	0.0441198i	$0.0140483\pi$
$379$			1.71784i			0.0882395i	−0.999026	+	0.0441198i	$0.985952\pi$
$380$		0			0
$381$	−16.0869	−	9.28776i	−0.824156	−	0.475827i
$382$		0			0
$383$	10.1017	+	2.70676i	0.516175	+	0.138309i	0.507497	−	0.861654i	$-0.330571\pi$
$383$	10.1017	+	2.70676i	0.516175	+	0.138309i	0.00867837	+	0.999962i	$0.497238\pi$
$384$		0			0
$385$	−4.35459	+	0.602485i	−0.221931	+	0.0307055i
$386$		0			0
$387$	−3.53225	−	0.946464i	−0.179554	−	0.0481114i
$388$		0			0
$389$	−18.8548	−	10.8858i	−0.955978	−	0.551934i	−0.0610449	−	0.998135i	$-0.519443\pi$
$389$	−18.8548	−	10.8858i	−0.955978	−	0.551934i	−0.894933	+	0.446201i	$0.852777\pi$
$390$		0			0
$391$			34.7124i			1.75548i
$392$		0			0
$393$	−7.96759	−	7.96759i	−0.401912	−	0.401912i
$394$		0			0
$395$	−14.6160	−	1.74410i	−0.735410	−	0.0877551i
$396$		0			0
$397$	−8.20427	+	30.6188i	−0.411761	+	1.53671i	0.379476	+	0.925202i	$0.376104\pi$
$397$	−8.20427	+	30.6188i	−0.411761	+	1.53671i	−0.791237	+	0.611510i	$0.790562\pi$
$398$		0			0
$399$	−5.10848	+	2.91170i	−0.255744	+	0.145767i
$400$		0			0
$401$	−6.98528	−	12.0989i	−0.348828	−	0.604188i	0.637213	−	0.770687i	$-0.280087\pi$
$401$	−6.98528	−	12.0989i	−0.348828	−	0.604188i	−0.986042	+	0.166499i	$0.946754\pi$
$402$		0			0
$403$	−9.60930	+	2.57480i	−0.478673	+	0.128260i
$404$		0			0
$405$	3.11146	−	1.33327i	0.154610	−	0.0662505i
$406$		0			0
$407$	1.40350	−	1.40350i	0.0695690	−	0.0695690i
$408$		0			0
$409$	9.36960	−	16.2286i	0.463297	−	0.802454i	−0.535826	−	0.844328i	$-0.680000\pi$
$409$	9.36960	−	16.2286i	0.463297	−	0.802454i	0.999123	+	0.0418748i	$0.0133330\pi$
$410$		0			0
$411$	9.47010	−	5.46757i	0.467126	−	0.269695i
$412$		0			0
$413$	4.79654	−	4.74360i	0.236022	−	0.233417i
$414$		0			0
$415$	28.9060	−	4.16294i	1.41894	−	0.204351i
$416$		0			0
$417$	−6.74040	−	25.1555i	−0.330079	−	1.23187i
$418$		0			0
$419$	−31.5744			−1.54251			−0.771255	−	0.636526i	$-0.780371\pi$
$419$	−31.5744			−1.54251			−0.771255	+	0.636526i	$0.780371\pi$
$420$		0			0
$421$	−13.5569			−0.660722			−0.330361	−	0.943855i	$-0.607171\pi$
$421$	−13.5569			−0.660722			−0.330361	+	0.943855i	$0.607171\pi$
$422$		0			0
$423$	1.97502	+	7.37087i	0.0960287	+	0.358384i
$424$		0			0
$425$	−17.0848	−	27.9999i	−0.828733	−	1.35820i
$426$		0			0
$427$	15.5445	−	4.07282i	0.752252	−	0.197097i
$428$		0			0
$429$	−2.19711	+	1.26850i	−0.106078	+	0.0612439i
$430$		0			0
$431$	6.63518	−	11.4925i	0.319605	−	0.553572i	−0.660800	−	0.750562i	$-0.729783\pi$
$431$	6.63518	−	11.4925i	0.319605	−	0.553572i	0.980406	+	0.196989i	$0.0631164\pi$
$432$		0			0
$433$	−12.0535	+	12.0535i	−0.579252	+	0.579252i	−0.934697	−	0.355445i	$-0.884329\pi$
$433$	−12.0535	+	12.0535i	−0.579252	+	0.579252i	0.355445	+	0.934697i	$0.384329\pi$
$434$		0			0
$435$	23.6334	+	9.45497i	1.13313	+	0.453331i
$436$		0			0
$437$	−9.67052	+	2.59121i	−0.462604	+	0.123954i
$438$		0			0
$439$	17.5238	+	30.3521i	0.836366	+	1.44863i	0.892913	+	0.450228i	$0.148657\pi$
$439$	17.5238	+	30.3521i	0.836366	+	1.44863i	−0.0565475	+	0.998400i	$0.518009\pi$
$440$		0			0
$441$	11.3413	+	0.125883i	0.540060	+	0.00599443i
$442$		0			0
$443$	0.0163232	−	0.0609189i	0.000775538	−	0.00289435i	−0.965537	−	0.260266i	$-0.916190\pi$
$443$	0.0163232	−	0.0609189i	0.000775538	−	0.00289435i	0.966313	+	0.257372i	$0.0828564\pi$
$444$		0			0
$445$	1.59817	−	13.3931i	0.0757606	−	0.634893i
$446$		0			0
$447$	−3.27444	−	3.27444i	−0.154876	−	0.154876i
$448$		0			0
$449$			24.5207i			1.15720i	0.815611	+	0.578601i	$0.196401\pi$
$449$			24.5207i			1.15720i	−0.815611	+	0.578601i	$0.803599\pi$
$450$		0			0
$451$	0.526205	+	0.303804i	0.0247780	+	0.0143056i
$452$		0			0
$453$	22.6298	+	6.06364i	1.06324	+	0.284894i
$454$		0			0
$455$	−17.0634	−	2.13224i	−0.799943	−	0.0999612i
$456$		0			0
$457$	−19.3892	−	5.19531i	−0.906987	−	0.243027i	−0.224973	−	0.974365i	$-0.572229\pi$
$457$	−19.3892	−	5.19531i	−0.906987	−	0.243027i	−0.682015	+	0.731339i	$0.738896\pi$
$458$		0			0
$459$	30.8324	+	17.8011i	1.43913	+	0.830884i
$460$		0			0
$461$			11.6940i			0.544642i	0.962207	+	0.272321i	$0.0877912\pi$
$461$			11.6940i			0.544642i	−0.962207	+	0.272321i	$0.912209\pi$
$462$		0			0
$463$	−2.77226	−	2.77226i	−0.128838	−	0.128838i	0.639747	−	0.768585i	$-0.279039\pi$
$463$	−2.77226	−	2.77226i	−0.128838	−	0.128838i	−0.768585	+	0.639747i	$0.779039\pi$
$464$		0			0
$465$	7.06489	−	5.55856i	0.327626	−	0.257772i
$466$		0			0
$467$	5.41472	−	20.2080i	0.250563	−	0.935116i	−0.719942	−	0.694035i	$-0.755831\pi$
$467$	5.41472	−	20.2080i	0.250563	−	0.935116i	0.970505	−	0.241081i	$-0.0775019\pi$
$468$		0			0
$469$	−0.201026	+	36.2233i	−0.00928250	+	1.67264i
$470$		0			0
$471$	4.38327	+	7.59205i	0.201971	+	0.349823i
$472$		0			0
$473$	−1.61992	+	0.434055i	−0.0744838	+	0.0199579i
$474$		0			0
$475$	6.52514	−	6.84976i	0.299394	−	0.314289i
$476$		0			0
$477$	−5.71218	+	5.71218i	−0.261543	+	0.261543i
$478$		0			0
$479$	−12.1419	+	21.0303i	−0.554775	+	0.960899i	0.443145	+	0.896450i	$0.353863\pi$
$479$	−12.1419	+	21.0303i	−0.554775	+	0.960899i	−0.997921	+	0.0644496i	$0.979471\pi$
$480$		0			0
$481$	6.72392	−	3.88206i	0.306584	−	0.177007i
$482$		0			0
$483$	−15.8602	−	4.34420i	−0.721663	−	0.197668i
$484$		0			0
$485$	−1.42755	−	9.91244i	−0.0648219	−	0.450101i
$486$		0			0
$487$	−0.661539	−	2.46890i	−0.0299772	−	0.111876i	0.949316	−	0.314323i	$-0.101777\pi$
$487$	−0.661539	−	2.46890i	−0.0299772	−	0.111876i	−0.979293	+	0.202446i	$0.935111\pi$
$488$		0			0
$489$	14.2910			0.646262
$490$		0			0
$491$	−14.5668			−0.657391			−0.328695	−	0.944436i	$-0.606609\pi$
$491$	−14.5668			−0.657391			−0.328695	+	0.944436i	$0.606609\pi$
$492$		0			0
$493$	16.4548	+	61.4102i	0.741088	+	2.76578i
$494$		0			0
$495$	−1.61287	+	2.15559i	−0.0724930	+	0.0968864i
$496$		0			0
$497$	40.8722	+	11.1951i	1.83337	+	0.502171i
$498$		0			0
$499$	−26.0565	+	15.0437i	−1.16645	+	0.673450i	−0.952841	−	0.303469i	$-0.901855\pi$
$499$	−26.0565	+	15.0437i	−1.16645	+	0.673450i	−0.213608	+	0.976919i	$0.568522\pi$
$500$		0			0
$501$	−1.20902	+	2.09409i	−0.0540152	+	0.0935572i
$502$		0			0
$503$	−24.6819	+	24.6819i	−1.10051	+	1.10051i	−0.106161	+	0.994349i	$0.533856\pi$
$503$	−24.6819	+	24.6819i	−1.10051	+	1.10051i	−0.994349	+	0.106161i	$0.966144\pi$
$504$		0			0
$505$	−9.84777	−	22.9819i	−0.438220	−	1.02268i
$506$		0			0
$507$	5.16386	−	1.38365i	0.229335	−	0.0614501i
$508$		0			0
$509$	−6.22521	−	10.7824i	−0.275927	−	0.477920i	0.694441	−	0.719549i	$-0.255652\pi$
$509$	−6.22521	−	10.7824i	−0.275927	−	0.477920i	−0.970369	+	0.241629i	$0.922318\pi$
$510$		0			0
$511$	0.129951	−	23.4162i	0.00574869	−	1.03587i
$512$		0			0
$513$	−2.65762	+	9.91839i	−0.117337	+	0.437908i
$514$		0			0
$515$	3.35456	+	4.26363i	0.147820	+	0.187878i
$516$		0			0
$517$	2.47458	+	2.47458i	0.108832	+	0.108832i
$518$		0			0
$519$		−	11.0509i		−	0.485079i
$520$		0			0
$521$	30.6011	+	17.6676i	1.34066	+	0.774030i	0.986904	−	0.161308i	$-0.0515711\pi$
$521$	30.6011	+	17.6676i	1.34066	+	0.774030i	0.353756	+	0.935338i	$0.384904\pi$
$522$		0			0
$523$	15.8804	+	4.25513i	0.694400	+	0.186064i	0.588721	−	0.808336i	$-0.299632\pi$
$523$	15.8804	+	4.25513i	0.694400	+	0.186064i	0.105679	+	0.994400i	$0.466298\pi$
$524$		0			0
$525$	14.9313	−	4.30192i	0.651657	−	0.187751i
$526$		0			0
$527$	21.6875	+	5.81115i	0.944722	+	0.253137i
$528$		0			0
$529$	−4.32938	−	2.49957i	−0.188234	−	0.108677i
$530$		0			0
$531$		−	4.13131i		−	0.179283i
$532$		0			0
$533$	1.68063	+	1.68063i	0.0727964	+	0.0727964i
$534$		0			0
$535$	9.18150	+	11.6696i	0.396951	+	0.504522i
$536$		0			0
$537$	−1.36729	+	5.10281i	−0.0590031	+	0.220202i
$538$		0			0
$539$	4.53322	−	2.55059i	0.195260	−	0.109862i
$540$		0			0
$541$	13.2572	+	22.9621i	0.569970	+	0.987218i	0.996568	+	0.0827763i	$0.0263787\pi$
$541$	13.2572	+	22.9621i	0.569970	+	0.987218i	−0.426598	+	0.904441i	$0.640288\pi$
$542$		0			0
$543$	20.2922	−	5.43727i	0.870820	−	0.233336i
$544$		0			0
$545$	7.89157	+	18.4167i	0.338038	+	0.788884i
$546$		0			0
$547$	1.07403	−	1.07403i	0.0459223	−	0.0459223i	−0.683773	−	0.729695i	$-0.739662\pi$
$547$	1.07403	−	1.07403i	0.0459223	−	0.0459223i	0.729695	+	0.683773i	$0.239662\pi$
$548$		0			0
$549$	4.92046	−	8.52249i	0.210000	−	0.363731i
$550$		0			0
$551$	−15.8799	+	9.16828i	−0.676507	+	0.390582i
$552$		0			0
$553$	16.8479	−	4.41431i	0.716444	−	0.187715i
$554$		0			0
$555$	−4.20311	+	5.61742i	−0.178412	+	0.238446i
$556$		0			0
$557$	4.02313	+	15.0145i	0.170466	+	0.636186i	0.997280	+	0.0737108i	$0.0234842\pi$
$557$	4.02313	+	15.0145i	0.170466	+	0.636186i	−0.826814	+	0.562475i	$0.809849\pi$
$558$		0			0
$559$	−6.56014			−0.277464
$560$		0			0
$561$	5.72584			0.241745
$562$		0			0
$563$	7.10355	+	26.5108i	0.299379	+	1.11730i	0.937677	+	0.347508i	$0.112972\pi$
$563$	7.10355	+	26.5108i	0.299379	+	1.11730i	−0.638298	+	0.769789i	$0.720361\pi$
$564$		0			0
$565$	−0.138742	−	0.963380i	−0.00583694	−	0.0405297i
$566$		0			0
$567$	−2.84784	+	2.81641i	−0.119598	+	0.118278i
$568$		0			0
$569$	−5.85207	+	3.37869i	−0.245332	+	0.141642i	−0.617625	−	0.786473i	$-0.711905\pi$
$569$	−5.85207	+	3.37869i	−0.245332	+	0.141642i	0.372293	+	0.928115i	$0.378572\pi$
$570$		0			0
$571$	5.87721	−	10.1796i	0.245953	−	0.426004i	−0.716446	−	0.697643i	$-0.754232\pi$
$571$	5.87721	−	10.1796i	0.245953	−	0.426004i	0.962399	+	0.271639i	$0.0875656\pi$
$572$		0			0
$573$	−2.30526	+	2.30526i	−0.0963034	+	0.0963034i
$574$		0			0
$575$	26.4493	−	0.641957i	1.10301	−	0.0267715i
$576$		0			0
$577$	2.17865	−	0.583767i	0.0906983	−	0.0243025i	−0.213184	−	0.977012i	$-0.568384\pi$
$577$	2.17865	−	0.583767i	0.0906983	−	0.0243025i	0.303883	+	0.952709i	$0.401717\pi$
$578$		0			0
$579$	−3.01879	−	5.22870i	−0.125457	−	0.217297i
$580$		0			0
$581$	−30.0209	+	17.1111i	−1.24547	+	0.709889i
$582$		0			0
$583$	−0.958858	+	3.57851i	−0.0397118	+	0.148207i
$584$		0			0
$585$	−8.27641	+	6.51177i	−0.342188	+	0.269229i
$586$		0			0
$587$	−12.8372	−	12.8372i	−0.529847	−	0.529847i	0.390680	−	0.920527i	$-0.372240\pi$
$587$	−12.8372	−	12.8372i	−0.529847	−	0.529847i	−0.920527	+	0.390680i	$0.872240\pi$
$588$		0			0
$589$			6.47569i			0.266826i
$590$		0			0
$591$	−1.92835	−	1.11333i	−0.0793218	−	0.0457965i
$592$		0			0
$593$	35.1170	+	9.40957i	1.44208	+	0.386405i	0.893262	−	0.449535i	$-0.148410\pi$
$593$	35.1170	+	9.40957i	1.44208	+	0.386405i	0.548820	+	0.835940i	$0.315077\pi$
$594$		0			0
$595$	30.9452	+	23.4230i	1.26863	+	0.960249i
$596$		0			0
$597$	−16.4549	−	4.40908i	−0.673455	−	0.180452i
$598$		0			0
$599$	−30.9792	−	17.8858i	−1.26578	−	0.730796i	−0.291589	−	0.956544i	$-0.594184\pi$
$599$	−30.9792	−	17.8858i	−1.26578	−	0.730796i	−0.974186	+	0.225748i	$0.927517\pi$
$600$		0			0
$601$		−	45.6631i		−	1.86264i	−0.364204	−	0.931319i	$-0.618659\pi$
$601$		−	45.6631i		−	1.86264i	0.364204	−	0.931319i	$-0.381341\pi$
$602$		0			0
$603$	15.6863	+	15.6863i	0.638796	+	0.638796i
$604$		0			0
$605$	2.76811	−	23.1975i	0.112540	−	0.943113i
$606$		0			0
$607$	0.303188	−	1.13151i	0.0123060	−	0.0459267i	−0.959500	−	0.281709i	$-0.909099\pi$
$607$	0.303188	−	1.13151i	0.0123060	−	0.0459267i	0.971806	+	0.235783i	$0.0757653\pi$
$608$		0			0
$609$	−30.1177	−	0.167142i	−1.22043	−	0.00677293i
$610$		0			0
$611$	6.84463	+	11.8553i	0.276904	+	0.479612i
$612$		0			0
$613$	13.4629	−	3.60737i	0.543760	−	0.145700i	0.0235253	−	0.999723i	$-0.492511\pi$
$613$	13.4629	−	3.60737i	0.543760	−	0.145700i	0.520235	+	0.854023i	$0.325844\pi$
$614$		0			0
$615$	−1.99404	−	0.797755i	−0.0804076	−	0.0321686i
$616$		0			0
$617$	22.7725	−	22.7725i	0.916788	−	0.916788i	−0.0800065	−	0.996794i	$-0.525494\pi$
$617$	22.7725	−	22.7725i	0.916788	−	0.916788i	0.996794	+	0.0800065i	$0.0254941\pi$
$618$		0			0
$619$	11.3386	−	19.6391i	0.455738	−	0.789361i	−0.542992	−	0.839738i	$-0.682709\pi$
$619$	11.3386	−	19.6391i	0.455738	−	0.789361i	0.998730	+	0.0503763i	$0.0160421\pi$
$620$		0			0
$621$	−24.8695	+	14.3584i	−0.997978	+	0.576183i
$622$		0			0
$623$	4.04497	+	15.4382i	0.162058	+	0.618520i
$624$		0			0
$625$	−21.0187	+	13.5356i	−0.840749	+	0.541425i
$626$		0			0
$627$	0.427421	+	1.59516i	0.0170696	+	0.0637045i
$628$		0			0
$629$	−17.5231			−0.698690
$630$		0			0
$631$	−32.4210			−1.29066			−0.645330	−	0.763904i	$-0.723280\pi$
$631$	−32.4210			−1.29066			−0.645330	+	0.763904i	$0.723280\pi$
$632$		0			0
$633$	3.04998	+	11.3827i	0.121226	+	0.452421i
$634$		0			0
$635$	−35.0004	+	5.04063i	−1.38895	+	0.200031i
$636$		0			0
$637$	19.7106	−	5.04765i	0.780963	−	0.199995i
$638$		0			0
$639$	22.4755	−	12.9762i	0.889116	−	0.513331i
$640$		0			0
$641$	0.428070	−	0.741439i	0.0169077	−	0.0292851i	−0.857448	−	0.514571i	$-0.827951\pi$
$641$	0.428070	−	0.741439i	0.0169077	−	0.0292851i	0.874355	+	0.485286i	$0.161285\pi$
$642$		0			0
$643$	16.4254	−	16.4254i	0.647754	−	0.647754i	−0.304696	−	0.952450i	$-0.598555\pi$
$643$	16.4254	−	16.4254i	0.647754	−	0.647754i	0.952450	+	0.304696i	$0.0985548\pi$
$644$		0			0
$645$	5.44871	−	2.33478i	0.214543	−	0.0919317i
$646$		0			0
$647$	45.8316	−	12.2805i	1.80183	−	0.482798i	0.807564	−	0.589779i	$-0.200785\pi$
$647$	45.8316	−	12.2805i	1.80183	−	0.482798i	0.994261	+	0.106982i	$0.0341186\pi$
$648$		0			0
$649$	−0.947323	−	1.64081i	−0.0371857	−	0.0644075i
$650$		0			0
$651$	−5.36927	+	9.18179i	−0.210438	+	0.359863i
$652$		0			0
$653$	6.80004	−	25.3781i	0.266106	−	0.993121i	−0.695464	−	0.718561i	$-0.744801\pi$
$653$	6.80004	−	25.3781i	0.266106	−	0.993121i	0.961570	−	0.274560i	$-0.0885323\pi$
$654$		0			0
$655$	−21.2991	−	2.54158i	−0.832225	−	0.0993077i
$656$		0			0
$657$	−10.1403	−	10.1403i	−0.395609	−	0.395609i
$658$		0			0
$659$			26.2355i			1.02199i	0.859583	+	0.510996i	$0.170723\pi$
$659$			26.2355i			1.02199i	−0.859583	+	0.510996i	$0.829277\pi$
$660$		0			0
$661$	−12.6197	−	7.28597i	−0.490848	−	0.283391i	0.234078	−	0.972218i	$-0.424793\pi$
$661$	−12.6197	−	7.28597i	−0.490848	−	0.283391i	−0.724926	+	0.688827i	$0.758126\pi$
$662$		0			0
$663$	21.6345	+	5.79695i	0.840215	+	0.225135i
$664$		0			0
$665$	−4.21541	+	10.3695i	−0.163466	+	0.402110i
$666$		0			0
$667$	−49.5336	−	13.2725i	−1.91795	−	0.513913i
$668$		0			0
$669$	−4.51371	−	2.60599i	−0.174510	−	0.100753i
$670$		0			0
$671$		−	4.51312i		−	0.174227i
$672$		0			0
$673$	−16.4201	−	16.4201i	−0.632950	−	0.632950i	0.315857	−	0.948807i	$-0.397708\pi$
$673$	−16.4201	−	16.4201i	−0.632950	−	0.632950i	−0.948807	+	0.315857i	$0.897708\pi$
$674$		0			0
$675$	12.9934	−	23.8221i	0.500117	−	0.916913i
$676$		0			0
$677$	−5.89172	+	21.9882i	−0.226437	+	0.845075i	0.755386	+	0.655280i	$0.227449\pi$
$677$	−5.89172	+	21.9882i	−0.226437	+	0.845075i	−0.981824	+	0.189796i	$0.939217\pi$
$678$		0			0
$679$	5.86774	+	10.2947i	0.225183	+	0.395076i
$680$		0			0
$681$	0.394008	+	0.682442i	0.0150984	+	0.0261512i
$682$		0			0
$683$	29.5964	−	7.93034i	1.13248	−	0.303446i	0.356554	−	0.934275i	$-0.383952\pi$
$683$	29.5964	−	7.93034i	1.13248	−	0.303446i	0.775922	+	0.630829i	$0.217285\pi$
$684$		0			0
$685$	7.73231	−	19.3274i	0.295436	−	0.738463i
$686$		0			0
$687$	−10.9664	+	10.9664i	−0.418394	+	0.418394i
$688$		0			0
$689$	−7.24590	+	12.5503i	−0.276047	+	0.478127i
$690$		0			0
$691$	−27.7284	+	16.0090i	−1.05484	+	0.609012i	−0.924000	−	0.382392i	$-0.875100\pi$
$691$	−27.7284	+	16.0090i	−1.05484	+	0.609012i	−0.130839	+	0.991404i	$0.541767\pi$
$692$		0			0
$693$	0.841516	−	3.07228i	0.0319665	−	0.116706i
$694$		0			0
$695$	−39.6952	−	29.7010i	−1.50573	−	1.12662i
$696$		0			0
$697$	−1.38836	−	5.18143i	−0.0525879	−	0.196261i
$698$		0			0
$699$	10.1709			0.384699
$700$		0			0
$701$	−18.5294			−0.699844			−0.349922	−	0.936779i	$-0.613792\pi$
$701$	−18.5294			−0.699844			−0.349922	+	0.936779i	$0.613792\pi$
$702$		0			0
$703$	−1.30806	−	4.88174i	−0.0493343	−	0.184118i
$704$		0			0
$705$	−9.90433	−	7.41068i	−0.373019	−	0.279103i
$706$		0			0
$707$	20.8025	+	21.0347i	0.782360	+	0.791092i
$708$		0			0
$709$	−23.1074	+	13.3411i	−0.867818	+	0.501035i	−0.866622	−	0.498965i	$-0.833714\pi$
$709$	−23.1074	+	13.3411i	−0.867818	+	0.501035i	−0.00119522	+	0.999999i	$0.500380\pi$
$710$		0			0
$711$	5.33302	−	9.23706i	0.200004	−	0.346417i
$712$		0			0
$713$	−12.8059	+	12.8059i	−0.479585	+	0.479585i
$714$		0			0
$715$	−1.79393	+	4.48406i	−0.0670893	+	0.167694i
$716$		0			0
$717$	4.54170	−	1.21695i	0.169613	−	0.0454477i
$718$		0			0
$719$	15.9890	+	27.6937i	0.596288	+	1.03280i	0.993364	+	0.115015i	$0.0366917\pi$
$719$	15.9890	+	27.6937i	0.596288	+	1.03280i	−0.397076	+	0.917786i	$0.629975\pi$
$720$		0			0
$721$	−5.54117	−	3.24033i	−0.206364	−	0.120676i
$722$		0			0
$723$	−5.26706	+	19.6569i	−0.195884	+	0.731049i
$724$		0			0
$725$	46.4875	−	13.6735i	1.72650	−	0.507822i
$726$		0			0
$727$	−21.4539	−	21.4539i	−0.795683	−	0.795683i	0.186729	−	0.982412i	$-0.440211\pi$
$727$	−21.4539	−	21.4539i	−0.795683	−	0.795683i	−0.982412	+	0.186729i	$0.940211\pi$
$728$		0			0
$729$			21.5770i			0.799146i
$730$		0			0
$731$	12.8222	+	7.40288i	0.474245	+	0.273805i
$732$		0			0
$733$	−12.5691	−	3.36789i	−0.464252	−	0.124396i	0.0191085	−	0.999817i	$-0.493917\pi$
$733$	−12.5691	−	3.36789i	−0.464252	−	0.124396i	−0.483360	+	0.875422i	$0.660584\pi$
$734$		0			0
$735$	−14.5747	+	11.2075i	−0.537597	+	0.413396i
$736$		0			0
$737$	9.82700	+	2.63314i	0.361982	+	0.0969928i
$738$		0			0
$739$	3.12136	+	1.80212i	0.114821	+	0.0662920i	0.556311	−	0.830974i	$-0.312216\pi$
$739$	3.12136	+	1.80212i	0.114821	+	0.0662920i	−0.441490	+	0.897266i	$0.645550\pi$
$740$		0			0
$741$			6.45988i			0.237309i
$742$		0			0
$743$	−31.1070	−	31.1070i	−1.14121	−	1.14121i	−0.988230	−	0.152977i	$-0.951114\pi$
$743$	−31.1070	−	31.1070i	−1.14121	−	1.14121i	−0.152977	−	0.988230i	$-0.548886\pi$
$744$		0			0
$745$	−8.75328	−	1.04451i	−0.320695	−	0.0382680i
$746$		0			0
$747$	−5.47705	+	20.4406i	−0.200395	+	0.747884i
$748$		0			0
$749$	−15.1663	−	8.86884i	−0.554164	−	0.324060i
$750$		0			0
$751$	−25.5141	−	44.1917i	−0.931023	−	1.61258i	−0.781576	−	0.623810i	$-0.785584\pi$
$751$	−25.5141	−	44.1917i	−0.931023	−	1.61258i	−0.149447	−	0.988770i	$-0.547749\pi$
$752$		0			0
$753$	6.23954	−	1.67188i	0.227382	−	0.0609267i
$754$		0			0
$755$	40.9941	−	17.5660i	1.49193	−	0.639293i
$756$		0			0
$757$	26.8141	−	26.8141i	0.974576	−	0.974576i	−0.0251083	−	0.999685i	$-0.507993\pi$
$757$	26.8141	−	26.8141i	0.974576	−	0.974576i	0.999685	+	0.0251083i	$0.00799305\pi$
$758$		0			0
$759$	−2.30924	+	3.99972i	−0.0838200	+	0.145181i
$760$		0			0
$761$	−25.8753	+	14.9391i	−0.937980	+	0.541543i	−0.889326	−	0.457273i	$-0.848826\pi$
$761$	−25.8753	+	14.9391i	−0.937980	+	0.541543i	−0.0486532	+	0.998816i	$0.515493\pi$
$762$		0			0
$763$	−16.6702	−	16.8563i	−0.603503	−	0.610239i
$764$		0			0
$765$	23.5250	−	3.38799i	0.850549	−	0.122493i
$766$		0			0
$767$	−1.91818	−	7.15874i	−0.0692614	−	0.258487i
$768$		0			0
$769$	44.7341			1.61315			0.806576	−	0.591130i	$-0.201318\pi$
$769$	44.7341			1.61315			0.806576	+	0.591130i	$0.201318\pi$
$770$		0			0
$771$	−19.3927			−0.698413
$772$		0			0
$773$	−6.25202	−	23.3328i	−0.224869	−	0.839224i	−0.982457	−	0.186490i	$-0.940289\pi$
$773$	−6.25202	−	23.3328i	−0.224869	−	0.839224i	0.757587	−	0.652734i	$-0.226378\pi$
$774$		0			0
$775$	4.02675	−	16.6324i	0.144645	−	0.597452i
$776$		0			0
$777$	2.19298	−	8.00631i	0.0786726	−	0.287225i
$778$		0			0
$779$	1.33985	−	0.773565i	0.0480052	−	0.0277158i
$780$		0			0
$781$	5.95099	−	10.3074i	0.212943	−	0.368828i
$782$		0			0
$783$	−37.1906	+	37.1906i	−1.32908	+	1.32908i
$784$		0			0
$785$	15.4945	+	6.19889i	0.553024	+	0.221248i
$786$		0			0
$787$	−12.2669	+	3.28689i	−0.437266	+	0.117165i	−0.470735	−	0.882275i	$-0.656011\pi$
$787$	−12.2669	+	3.28689i	−0.437266	+	0.117165i	0.0334688	+	0.999440i	$0.489345\pi$
$788$		0			0
$789$	5.79134	+	10.0309i	0.206177	+	0.357110i
$790$		0			0
$791$	0.570279	+	1.00054i	0.0202768	+	0.0355749i
$792$		0			0
$793$	4.56917	−	17.0524i	0.162256	−	0.605547i
$794$		0			0
$795$	1.55160	−	13.0028i	0.0550296	−	0.461163i
$796$		0			0
$797$	−8.99183	−	8.99183i	−0.318507	−	0.318507i	0.529687	−	0.848193i	$-0.322310\pi$
$797$	−8.99183	−	8.99183i	−0.318507	−	0.318507i	−0.848193	+	0.529687i	$0.822310\pi$
$798$		0			0
$799$		−	30.8957i		−	1.09301i
$800$		0			0
$801$	8.46421	+	4.88682i	0.299068	+	0.172667i
$802$		0			0
$803$	−6.35256	−	1.70216i	−0.224177	−	0.0600681i
$804$		0			0
$805$	−28.8421	+	12.1699i	−1.01655	+	0.428931i
$806$		0			0
$807$	10.1642	+	2.72348i	0.357796	+	0.0958710i
$808$		0			0
$809$	23.7782	+	13.7284i	0.835997	+	0.482663i	0.855902	−	0.517139i	$-0.173003\pi$
$809$	23.7782	+	13.7284i	0.835997	+	0.482663i	−0.0199044	+	0.999802i	$0.506336\pi$
$810$		0			0
$811$			12.7335i			0.447132i	0.974689	+	0.223566i	$0.0717699\pi$
$811$			12.7335i			0.447132i	−0.974689	+	0.223566i	$0.928230\pi$
$812$		0			0
$813$	−18.9789	−	18.9789i	−0.665620	−	0.665620i
$814$		0			0
$815$	21.3808	−	16.8221i	0.748938	−	0.589254i
$816$		0			0
$817$	−1.10522	+	4.12473i	−0.0386666	+	0.144306i
$818$		0			0
$819$	6.29002	−	10.7563i	0.219791	−	0.375857i
$820$		0			0
$821$	−15.1707	−	26.2764i	−0.529461	−	0.917054i	−0.999410	−	0.0343601i	$-0.989061\pi$
$821$	−15.1707	−	26.2764i	−0.529461	−	0.917054i	0.469948	−	0.882694i	$-0.344273\pi$
$822$		0			0
$823$	9.82702	−	2.63314i	0.342549	−	0.0917856i	−0.0834435	−	0.996513i	$-0.526592\pi$
$823$	9.82702	−	2.63314i	0.342549	−	0.0917856i	0.425992	+	0.904727i	$0.359925\pi$
$824$		0			0
$825$	−0.105891	−	4.36283i	−0.00368666	−	0.151894i
$826$		0			0
$827$	15.9794	−	15.9794i	0.555660	−	0.555660i	−0.372409	−	0.928069i	$-0.621468\pi$
$827$	15.9794	−	15.9794i	0.555660	−	0.555660i	0.928069	+	0.372409i	$0.121468\pi$
$828$		0			0
$829$	3.17447	−	5.49835i	0.110254	−	0.190966i	−0.805619	−	0.592435i	$-0.798167\pi$
$829$	3.17447	−	5.49835i	0.110254	−	0.190966i	0.915873	+	0.401469i	$0.131500\pi$
$830$		0			0
$831$	21.9046	−	12.6466i	0.759861	−	0.438706i
$832$		0			0
$833$	−44.2216	−	12.3768i	−1.53219	−	0.428830i
$834$		0			0
$835$	0.656159	+	4.55614i	0.0227073	+	0.157672i
$836$		0			0
$837$	4.80743	+	17.9416i	0.166169	+	0.620151i
$838$		0			0
$839$	39.7411			1.37202			0.686008	−	0.727594i	$-0.259362\pi$
$839$	39.7411			1.37202			0.686008	+	0.727594i	$0.259362\pi$
$840$		0			0
$841$	−64.9222			−2.23870
$842$		0			0
$843$	1.71732	+	6.40914i	0.0591478	+	0.220742i
$844$		0			0
$845$	6.09695	−	8.14853i	0.209741	−	0.280318i
$846$		0			0
$847$	7.00609	+	26.7398i	0.240732	+	0.918790i
$848$		0			0
$849$	2.97899	−	1.71992i	0.102239	−	0.0590276i
$850$		0			0
$851$	7.06707	−	12.2405i	0.242256	−	0.419600i
$852$		0			0
$853$	−17.1451	+	17.1451i	−0.587036	+	0.587036i	−0.936828	−	0.349791i	$-0.886252\pi$
$853$	−17.1451	+	17.1451i	−0.587036	+	0.587036i	0.349791	+	0.936828i	$0.386252\pi$
$854$		0			0
$855$	2.69995	+	6.30091i	0.0923363	+	0.215487i
$856$		0			0
$857$	16.2677	−	4.35890i	0.555692	−	0.148897i	0.0299658	−	0.999551i	$-0.490460\pi$
$857$	16.2677	−	4.35890i	0.555692	−	0.148897i	0.525727	+	0.850654i	$0.323794\pi$
$858$		0			0
$859$	−15.4345	−	26.7333i	−0.526619	−	0.912130i	−0.999519	−	0.0310142i	$-0.990126\pi$
$859$	−15.4345	−	26.7333i	−0.526619	−	0.912130i	0.472900	−	0.881116i	$-0.343207\pi$
$860$		0			0
$861$	2.54115	+	0.0141024i	0.0866023	+	0.000480610i
$862$		0			0
$863$	0.334691	−	1.24908i	0.0113930	−	0.0425193i	−0.959995	−	0.280016i	$-0.909660\pi$
$863$	0.334691	−	1.24908i	0.0113930	−	0.0425193i	0.971388	+	0.237497i	$0.0763269\pi$
$864$		0			0
$865$	−13.0081	−	16.5332i	−0.442289	−	0.562147i
$866$		0			0
$867$	−21.6244	−	21.6244i	−0.734404	−	0.734404i
$868$		0			0
$869$		−	4.89152i		−	0.165934i
$870$		0			0
$871$	34.4645	+	19.8981i	1.16778	+	0.674221i
$872$		0			0
$873$	7.00950	+	1.87819i	0.237236	+	0.0635671i
$874$		0			0
$875$	17.2750	−	24.0120i	0.584001	−	0.811753i
$876$		0			0
$877$	−9.37406	−	2.51177i	−0.316540	−	0.0848165i	0.0970513	−	0.995279i	$-0.469059\pi$
$877$	−9.37406	−	2.51177i	−0.316540	−	0.0848165i	−0.413591	+	0.910463i	$0.635726\pi$
$878$		0			0
$879$	−15.5189	−	8.95985i	−0.523440	−	0.302208i
$880$		0			0
$881$			18.3500i			0.618227i	0.951025	+	0.309113i	$0.100032\pi$
$881$			18.3500i			0.618227i	−0.951025	+	0.309113i	$0.899968\pi$
$882$		0			0
$883$	−23.7527	−	23.7527i	−0.799342	−	0.799342i	0.183650	−	0.982992i	$-0.441209\pi$
$883$	−23.7527	−	23.7527i	−0.799342	−	0.799342i	−0.982992	+	0.183650i	$0.941209\pi$
$884$		0			0
$885$	4.14102	+	5.26320i	0.139199	+	0.176921i
$886$		0			0
$887$	−10.0547	+	37.5247i	−0.337604	+	1.25996i	0.563414	+	0.826175i	$0.309488\pi$
$887$	−10.0547	+	37.5247i	−0.337604	+	1.25996i	−0.901018	+	0.433781i	$0.857179\pi$
$888$		0			0
$889$	36.3503	−	20.7187i	1.21915	−	0.694884i
$890$		0			0
$891$	0.562452	+	0.974195i	0.0188429	+	0.0326368i
$892$		0			0
$893$	8.60721	−	2.30629i	0.288029	−	0.0771772i
$894$		0			0
$895$	3.96097	+	9.24379i	0.132401	+	0.308986i
$896$		0			0
$897$	−12.7746	+	12.7746i	−0.426532	+	0.426532i
$898$		0			0
$899$	−16.5847	+	28.7255i	−0.553130	+	0.958049i
$900$		0			0
$901$	28.3251	−	16.3535i	0.943644	−	0.544813i
$902$		0			0
$903$	−4.98705	+	4.93201i	−0.165959	+	0.164127i
$904$		0			0
$905$	23.9589	−	32.0209i	0.796421	−	1.06441i
$906$		0			0
$907$	−8.97748	−	33.5044i	−0.298092	−	1.11250i	−0.938730	−	0.344653i	$-0.887997\pi$
$907$	−8.97748	−	33.5044i	−0.298092	−	1.11250i	0.640638	−	0.767843i	$-0.278670\pi$
$908$		0			0
$909$	18.1174			0.600916
$910$		0			0
$911$	−48.1523			−1.59536			−0.797678	−	0.603083i	$-0.793939\pi$
$911$	−48.1523			−1.59536			−0.797678	+	0.603083i	$0.793939\pi$
$912$		0			0
$913$	2.51182	+	9.37422i	0.0831290	+	0.310242i
$914$		0			0
$915$	2.27395	+	15.7895i	0.0751744	+	0.521985i
$916$		0			0
$917$	24.5515	−	6.43273i	0.810761	−	0.212428i
$918$		0			0
$919$	−15.4242	+	8.90515i	−0.508797	+	0.293754i	−0.732339	−	0.680940i	$-0.761571\pi$
$919$	−15.4242	+	8.90515i	−0.508797	+	0.293754i	0.223542	+	0.974694i	$0.428238\pi$
$920$		0			0
$921$	5.72435	−	9.91487i	0.188624	−	0.326706i
$922$		0			0
$923$	32.9206	−	32.9206i	1.08360	−	1.08360i
$924$		0			0
$925$	0.324064	+	13.3518i	0.0106552	+	0.439004i
$926$		0			0
$927$	−3.79713	+	1.01744i	−0.124714	+	0.0334171i
$928$		0			0
$929$	16.1326	+	27.9424i	0.529292	+	0.916761i	0.999416	+	0.0341607i	$0.0108758\pi$
$929$	16.1326	+	27.9424i	0.529292	+	0.916761i	−0.470124	+	0.882600i	$0.655791\pi$
$930$		0			0
$931$	0.146998	−	13.2436i	0.00481766	−	0.434040i
$932$		0			0
$933$	0.0383114	−	0.142980i	0.00125426	−	0.00468096i
$934$		0			0
$935$	8.56645	−	6.73996i	0.280153	−	0.220420i
$936$		0			0
$937$	−28.9650	−	28.9650i	−0.946244	−	0.946244i	0.0523829	−	0.998627i	$-0.483318\pi$
$937$	−28.9650	−	28.9650i	−0.946244	−	0.946244i	−0.998627	+	0.0523829i	$0.983318\pi$
$938$		0			0
$939$			13.7359i			0.448254i
$940$		0			0
$941$	30.8629	+	17.8187i	1.00610	+	0.580874i	0.910048	−	0.414502i	$-0.136044\pi$
$941$	30.8629	+	17.8187i	1.00610	+	0.580874i	0.0960550	+	0.995376i	$0.469378\pi$
$942$		0			0
$943$	4.17936	+	1.11985i	0.136099	+	0.0364675i
$944$		0			0
$945$	−3.98112	+	31.8591i	−0.129506	+	1.03638i
$946$		0			0
$947$	13.4783	+	3.61149i	0.437985	+	0.117358i	0.471072	−	0.882095i	$-0.343867\pi$
$947$	13.4783	+	3.61149i	0.437985	+	0.117358i	−0.0330871	+	0.999452i	$0.510534\pi$
$948$		0			0
$949$	−22.2792	−	12.8629i	−0.723214	−	0.417548i
$950$		0			0
$951$		−	12.8576i		−	0.416935i
$952$		0			0
$953$	25.4475	+	25.4475i	0.824326	+	0.824326i	0.986725	−	0.162399i	$-0.0519232\pi$
$953$	25.4475	+	25.4475i	0.824326	+	0.824326i	−0.162399	+	0.986725i	$0.551923\pi$
$954$		0			0
$955$	−0.735353	+	6.16245i	−0.0237955	+	0.199412i
$956$		0			0
$957$	−2.18931	+	8.17061i	−0.0707703	+	0.264118i
$958$		0			0
$959$	−0.136689	+	24.6304i	−0.00441392	+	0.795356i
$960$		0			0
$961$	−9.64300	−	16.7022i	−0.311064	−	0.538779i
$962$		0			0
$963$	−10.3928	+	2.78475i	−0.334904	+	0.0897373i
$964$		0			0
$965$	−10.6712	−	4.26922i	−0.343518	−	0.137431i
$966$		0			0
$967$	34.0735	−	34.0735i	1.09573	−	1.09573i	0.100827	−	0.994904i	$-0.467851\pi$
$967$	34.0735	−	34.0735i	1.09573	−	1.09573i	0.994904	−	0.100827i	$-0.0321488\pi$
$968$		0			0
$969$	7.28974	−	12.6262i	0.234180	−	0.405612i
$970$		0			0
$971$	−4.07547	+	2.35297i	−0.130788	+	0.0755105i	−0.563966	−	0.825798i	$-0.690725\pi$
$971$	−4.07547	+	2.35297i	−0.130788	+	0.0755105i	0.433179	+	0.901308i	$0.357392\pi$
$972$		0			0
$973$	56.5762	+	15.4966i	1.81375	+	0.496797i
$974$		0			0
$975$	4.01692	−	16.5917i	0.128644	−	0.531361i
$976$		0			0
$977$	−7.12351	−	26.5853i	−0.227901	−	0.850540i	−0.981221	−	0.192885i	$-0.938215\pi$
$977$	−7.12351	−	26.5853i	−0.227901	−	0.850540i	0.753320	−	0.657654i	$-0.228451\pi$
$978$		0			0
$979$	4.48226			0.143254
$980$		0			0
$981$	−14.5185			−0.463539
$982$		0			0
$983$	−11.6256	−	43.3874i	−0.370799	−	1.38384i	−0.859386	−	0.511327i	$-0.829154\pi$
$983$	−11.6256	−	43.3874i	−0.370799	−	1.38384i	0.488587	−	0.872515i	$-0.337513\pi$
$984$		0			0
$985$	−4.19554	+	0.604226i	−0.133681	+	0.0192522i
$986$		0			0
$987$	14.1163	+	3.86654i	0.449326	+	0.123073i
$988$		0			0
$989$	−10.3424	+	5.97118i	−0.328869	+	0.189872i
$990$		0			0
$991$	−3.08498	+	5.34334i	−0.0979975	+	0.169737i	−0.910856	−	0.412725i	$-0.864577\pi$
$991$	−3.08498	+	5.34334i	−0.0979975	+	0.169737i	0.812858	+	0.582462i	$0.197910\pi$
$992$		0			0
$993$	−4.53527	+	4.53527i	−0.143922	+	0.143922i
$994$		0			0
$995$	−29.8083	+	12.7729i	−0.944985	+	0.404927i
$996$		0			0
$997$	18.1820	−	4.87184i	0.575829	−	0.154293i	0.0408602	−	0.999165i	$-0.486990\pi$
$997$	18.1820	−	4.87184i	0.575829	−	0.154293i	0.534968	+	0.844872i	$0.320324\pi$
$998$		0			0
$999$	−7.24821	−	12.5543i	−0.229323	−	0.397199i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	560.2.ci.c.353.2		16
4.3	odd	2		70.2.k.a.3.4	✓	16
5.2	odd	4	inner	560.2.ci.c.17.2		16
7.5	odd	6	inner	560.2.ci.c.33.2		16
12.11	even	2		630.2.bv.c.73.2		16
20.3	even	4		350.2.o.c.157.3		16
20.7	even	4		70.2.k.a.17.2	yes	16
20.19	odd	2		350.2.o.c.143.1		16
28.3	even	6		490.2.g.c.293.2		16
28.11	odd	6		490.2.g.c.293.3		16
28.19	even	6		70.2.k.a.33.2	yes	16
28.23	odd	6		490.2.l.c.313.1		16
28.27	even	2		490.2.l.c.423.3		16
35.12	even	12	inner	560.2.ci.c.257.2		16
60.47	odd	4		630.2.bv.c.577.3		16
84.47	odd	6		630.2.bv.c.523.3		16
140.19	even	6		350.2.o.c.243.3		16
140.27	odd	4		490.2.l.c.227.1		16
140.47	odd	12		70.2.k.a.47.4	yes	16
140.67	even	12		490.2.g.c.97.2		16
140.87	odd	12		490.2.g.c.97.3		16
140.103	odd	12		350.2.o.c.257.1		16
140.107	even	12		490.2.l.c.117.3		16
420.47	even	12		630.2.bv.c.397.2		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
70.2.k.a.3.4	✓	16	4.3	odd	2
70.2.k.a.17.2	yes	16	20.7	even	4
70.2.k.a.33.2	yes	16	28.19	even	6
70.2.k.a.47.4	yes	16	140.47	odd	12
350.2.o.c.143.1		16	20.19	odd	2
350.2.o.c.157.3		16	20.3	even	4
350.2.o.c.243.3		16	140.19	even	6
350.2.o.c.257.1		16	140.103	odd	12
490.2.g.c.97.2		16	140.67	even	12
490.2.g.c.97.3		16	140.87	odd	12
490.2.g.c.293.2		16	28.3	even	6
490.2.g.c.293.3		16	28.11	odd	6
490.2.l.c.117.3		16	140.107	even	12
490.2.l.c.227.1		16	140.27	odd	4
490.2.l.c.313.1		16	28.23	odd	6
490.2.l.c.423.3		16	28.27	even	2
560.2.ci.c.17.2		16	5.2	odd	4	inner
560.2.ci.c.33.2		16	7.5	odd	6	inner
560.2.ci.c.257.2		16	35.12	even	12	inner
560.2.ci.c.353.2		16	1.1	even	1	trivial
630.2.bv.c.73.2		16	12.11	even	2
630.2.bv.c.397.2		16	420.47	even	12
630.2.bv.c.523.3		16	84.47	odd	6
630.2.bv.c.577.3		16	60.47	odd	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 560 = 2^{4} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	560.ci (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.304013 - 1.13459i) q^{3} +(-1.79038 - 1.33961i) q^{5} +(2.55176 + 0.698943i) q^{7} +(1.40320 - 0.810140i) q^{9} +O(q^{10})\)	\(q+(-0.304013 - 1.13459i) q^{3} +(-1.79038 - 1.33961i) q^{5} +(2.55176 + 0.698943i) q^{7} +(1.40320 - 0.810140i) q^{9} +(0.371536 - 0.643519i) q^{11} +(2.05532 - 2.05532i) q^{13} +(-0.975610 + 2.43860i) q^{15} +(-6.33660 + 1.69789i) q^{17} +(-0.946027 - 1.63857i) q^{19} +(0.0172465 - 3.10769i) q^{21} +(1.36952 - 5.11112i) q^{23} +(1.41090 + 4.79681i) q^{25} +(-3.83750 - 3.83750i) q^{27} -9.69135i q^{29} +(-2.96403 - 1.71129i) q^{31} +(-0.843083 - 0.225903i) q^{33} +(-3.63230 - 4.66973i) q^{35} +(2.58012 + 0.691342i) q^{37} +(-2.95680 - 1.70711i) q^{39} +0.817699i q^{41} +(-1.59589 - 1.59589i) q^{43} +(-3.59753 - 0.429287i) q^{45} +(-1.21894 + 4.54913i) q^{47} +(6.02296 + 3.56707i) q^{49} +(3.85282 + 6.67328i) q^{51} +(-4.81583 + 1.29040i) q^{53} +(-1.52725 + 0.654429i) q^{55} +(-1.57150 + 1.57150i) q^{57} +(1.27487 - 2.20815i) q^{59} +(5.25989 - 3.03680i) q^{61} +(4.14688 - 1.08652i) q^{63} +(-6.43313 + 0.926476i) q^{65} +(3.54358 + 13.2248i) q^{67} -6.21538 q^{69} +16.0173 q^{71} +(-2.29071 - 8.54906i) q^{73} +(5.01348 - 3.05909i) q^{75} +(1.39785 - 1.38242i) q^{77} +(5.70091 - 3.29142i) q^{79} +(-0.756928 + 1.31104i) q^{81} +(-9.23519 + 9.23519i) q^{83} +(13.6194 + 5.44871i) q^{85} +(-10.9957 + 2.94629i) q^{87} +(3.01603 + 5.22392i) q^{89} +(6.68124 - 3.80814i) q^{91} +(-1.04051 + 3.88322i) q^{93} +(-0.501292 + 4.20096i) q^{95} +(3.16693 + 3.16693i) q^{97} -1.20398i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 12 q^{5} - 8 q^{7}+O(q^{10}) \) 16 * q - 12 * q^5 - 8 * q^7	\( 16 q - 12 q^{5} - 8 q^{7} + 12 q^{11} - 16 q^{15} - 36 q^{17} - 28 q^{21} + 4 q^{23} + 12 q^{25} - 24 q^{31} + 48 q^{33} - 8 q^{35} + 4 q^{37} + 8 q^{43} - 12 q^{45} - 12 q^{47} + 16 q^{51} - 28 q^{53} + 8 q^{57} - 12 q^{61} + 36 q^{63} - 8 q^{65} - 32 q^{67} - 16 q^{71} - 12 q^{73} + 48 q^{75} + 16 q^{77} + 24 q^{85} + 24 q^{87} + 16 q^{91} + 28 q^{93} - 20 q^{95}+O(q^{100}) \) 16 * q - 12 * q^5 - 8 * q^7 + 12 * q^11 - 16 * q^15 - 36 * q^17 - 28 * q^21 + 4 * q^23 + 12 * q^25 - 24 * q^31 + 48 * q^33 - 8 * q^35 + 4 * q^37 + 8 * q^43 - 12 * q^45 - 12 * q^47 + 16 * q^51 - 28 * q^53 + 8 * q^57 - 12 * q^61 + 36 * q^63 - 8 * q^65 - 32 * q^67 - 16 * q^71 - 12 * q^73 + 48 * q^75 + 16 * q^77 + 24 * q^85 + 24 * q^87 + 16 * q^91 + 28 * q^93 - 20 * q^95

Introduction

L-functions

Modular forms

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Representations

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Database

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